A DC-DC converter controls a supply current (IIN) provided to a rechargeable battery. The converter comprises an electrical input terminal that receives supply current (IIN). An electrical output terminal is connected to the battery through a coil with a resistor in series therebetween. A controllable selector connects the input terminal to the output terminal during a first time interval in order to supply the battery and to connect the input terminal to a ground potential during a successive second time interval. Also, a feedback module generates a control signal for the selector from a resistor feedback signal, indicative of a variation of a battery charge current (IOUT). The feedback module has an electronic block that receives the feedback signal. The electronic block processes the feedback signal to measure a variation of the supply current (IIN) and provide the control signal to adjust the duration of the first time interval.